As the definition implies, analogy involves an extensive use of types; let us, therefore, become better acquainted with them as instruments in analogical inductions. A type is _one_ of a group which embodies the _essential characteristics_ of that group. How easy and natural it is to dismiss a complex topic with the citing of an example which may be regarded as a type; how common is the use of examples in the school room! On second thought it becomes apparent that analogical induction by example or type is the most common of all forms of induction either as a method or a mode of inference. _Analogy by example (or type) assumes that if two or more things are of the same type, they resemble each other in every essential property._ Illustrations of analogical inductions by example or type. (1) _Mathematics._ Example: a + b a + b ――――――――――――― a² + ab + ab + b² ――――――――――――― a² + 2ab + b² Inductive Inference: The square of the sum of two quantities is equal to the square of the first, plus twice the first by the second, plus the square of the second. (2) _Nature._ This corn sent me as a sample produced heavy, full ears, and many of them; hence (inductive inference), if I plant corn _like this sample_ under like conditions, I will receive in return heavy, full ears, and many of them. (3) _Geography._ Cities like New York, located on the coast, possess a larger foreign element than the inland cities like Philadelphia. (4) _Grammar._ A noun is the name of anything, as the examples, “George Washington” and “house” would indicate. In deriving a generalization from one or two examples the prime essential is to select types which are _truly representative_. Often the example used is a special type and in consequence does not exemplify all of the essential characteristics of the group. To teach the nature of a parallelogram by using a rectangle only, is an easy way to commit this error; or one may affirm that the class can easily cover the work, when the judgment is based entirely on knowledge concerning the _brightest_ one of the grade. Type work when judicially used is a positive time saver and a very present help in times of perplexity. Let the skillful teacher use types and examples extensively yet cautiously. THE MARK OF SIMILARITY. As opposed to analogy by type there is a second form; namely, _analogy by one or more similar marks or qualities_. This form is best described by the definition: _When two things resemble each other in a few marks or qualities they resemble each other in other marks or qualities._ Illustrations of analogy by marks. (1) Noting that two students have the same surname, I infer that they are brothers. (2) A man with a book under his arm rings the door bell and asks to see “the lady of the house.” At once the conclusion is drawn that the caller is a book agent.